Theorem: Reference-preserving target-adapted transport

After hop $j$, every payload-reference input has state

The logical channel from $X_0$ to $X_n$ is exactly ${\mathrm{id}}_{{\mathbb{C}}^4}$, including every reference. Arrival is at $T_{\mathrm{d}}+L/c$. All tick-boundary communication dependencies are causal in the prescribed background.

Proof. The first SWAP transfers the entire input factor, including all reference correlations, into the next independent blank. Induction proves the displayed state identity.

Each hop has spatial length $L/n=c\delta T$. Its developed straight path is null, and convexity keeps the route in the regular chart. Pullback by the local isometry therefore gives a causal route in $(M,\bar{g})$.